With the coming of big data age, the data usually present in a huge magnitude such as TB or more. These data contain both useful and useless information. Therefore, techniques which can effectively analyze these data are in urgent demand. In practice, dealing with Electroencephalographic (EEG) signals with Independent Component Analysis (ICA) approximates to a big optimization problem because it requires real-time, or at least automatic in dealing with signals. Thus, in the Optimization of Big Data 2015 Competition, the problem abstracted from dealing with EEG signals through ICA is modeled as a big optimization problem (BigOpt). Evolutionary optimization techniques have been successfully used in solving various optimization problems, and in the age of big data, they have attracted increasing attentions. Since the multi-agent genetic algorithm (MAGA) shows a good performance in solving large-scale problems, in this paper, based on the framework of MAGA, an MAGA is proposed for solving the big optimization problem, which is labeled as MAGA-BigOpt. In MAGA-BigOpt, the competition and self-learning operators are redesigned and combined with crossover and mutation operators to simulate the cooperation, competition, and learning behaviors of agents. Especially, in the self-learning operator, agents quickly find decreasing directions to improve itself with a heuristic strategy. In the experiments, the performance of MAGA-BigOpt is validated on the given benchmark problems from the Optimization of Big Data 2015 Competition, where both the data with and without noise are used. The results show that MAGA-BigOpt outperforms the baseline algorithm provided by the competition in both cases with lower computational costs.